M.B.A. DEGREE EXAMINATION, JUNE 2010

First Semester

BA9201 — STATISTICS FOR MANAGEMENT

(Regulation 2009)

Time : Three hours Maximum : 100 Marks

Statistical Table Book need to be provided

Answer ALL Questions

PART A — (10 × 2 = 20 Marks)

1. Distinguish between qualitative and quantitative variables in statistics.

2. Name four descriptive statistics used.3. What is a sampling distribution?

4. Give two rules for determining sample size.

5. What is a hypothesis?

6. What is meant by design of experiments?

7. What is a non-parametric test?

8. When is Kruskal-Wallis test used?

9. When is regression used?

10. What is an index number?

PART B — (5 × 16 = 80 Marks)

11. (a) The following information regarding the top ten Fortune 500 companies was presented

in an issue of Fortune Magazine.

Company Sales

$ Millions

Sales

Rank

Profits

$ Millions

Profits

Rank

General Motors 161,315 1 2,956 30

Ford Motor 144,416 2 22,071 2

Wal-Mart Stores 139,208 3 4,430 14

Exxon 100,697 4 6,370 5

General Electric 100,469 5 9,269 3

Int'l Business Machines 81,667 6 6,328 6

Citigroup 76,431 7 5,807 8

Philip Morris 57,813 8 5,372 9

Boeing 56,154 9 1,120 82

AT and T 53,588 10 6,398 4

(i) How many elements are in the above data set?

(ii) How many variables are in this data set?

(iii) How many observations are in this data set?

(iv) Which variables are qualitative and which are quantitative variables?

(v) What measurement scale is used for each variable?

Or

(b) In the two upcoming basketball games (involving A & B and A & C), the probability

that A will defeat B is 0.63, and the probability that A will defeat C is 0.55. The

probability that A will defeat both opponents is 0.3465.

(i) What is the probability that A will defeat C given that they defeat B?

(ii) What is the probability that A will win at least one of the games?

(iii) What is the probability of A winning both games?

(iv) Are the outcomes of the games independent? Explain and substantiate your

answer.

12. (a) The values obtained from a random sample of 4 observations taken from an infinite

population are given below:

32, 34, 35, 39

(i) Find a point estimate for . µ Is this an unbiased estimate of µ? Explain.

(ii) Find a point estimate for 2

σ . Is this an unbiased estimated of 2

σ ? Explain.

(iii) Find a point estimate for . σ

(iv) What can be said about the sampling distribution of x ? Discuss the expected

value, the standard deviation, and the shape of the sampling distribution of x .

Or

(b) A bank has kept records of the checking balances of its customers and determined that

the average daily balance of its customers is $300 with a standard deviation of $48. A

random sample of 144 checking accounts is selected.

(i) What is probability that the sample mean will be more than $306.60?

(ii) What is probability that the sample mean will be less than $308?

(iii) What is probability that the sample mean will be between $302 and $308?

(iv) What is the probability that the sample mean will be at least $296?

13. (a) The following is the information obtained from a random sample of 5 observations.

Assume the population has a normal distribution.

20, 18, 17, 22, 18

It is required to determine whether or not the mean of the population from which this

sample was taken is significantly less than 21

(i) State the null and the alternative hypotheses.

(ii) Compute the standard error of the mean.

(iii) Determine the test statistic.

(iv) Determine the − p value and at 90% confidence, test whether or not the mean of

the population is significantly less than 21.

Or

(b) In order to test to see if there is any significant difference in the mean number of units

produced per week by each of three production methods, the following data were

collected. (Note that the sample sizes are not equal.)

Method I Method II Method III

182 170 162

170 192 166

179 190

(i) Compute x .

(ii) At the α= 0.05 level of significance, is there any difference in the mean number of

units produced per week by each method? Show the complete ANOVA table. Use

both the critical and p -value approaches.

14. (a) Independent random samples of ten day students and ten evening students at a

University showed the following age distributions. We want to use the Mann-Whitney-

Wilcoxon test to determine if there is a significant difference in the age distribution of

the two groups.

Day Evening

26 32

18 24

25 23

27 30

19 40

30 41

34 42

21 39

33 45

31 35

(i) Compute the sum of the ranks (T) for the day students.

(ii) Compute the mean . T µ

(iii) Compute . T σ

(iv) Use 05 . 0 = α and test for any significant differences in the age distribution of the

two populations.

Or

(b) In a sample of 400 people, 250 indicated that they prefer domestic products, while 140

said they prefer foreign products, and 10 indicated no preference. We want to use the

sign test to determine if there is evidence of a significant difference in the preferences

for the two types of products.

(i) Provide the hypotheses to be tested.

(ii) Compute the mean.

(iii) Compute the standard deviation.

132 132 132

J6501 4

(iv) At 95% confidence, test to determine if there is evidence of a significant difference

in the preferences for the two types of products.

15. (a) A coffee shop owner believes that the sales of coffee at his coffee shop depend upon the

weather. He has taken a sample of 6 days. The results of the sample are given below.

Cups of Coffee Sold Temperature

350 50

200 60

210 70

100 80

60 90

40 100

(i) Which variable is the dependent variable?

(ii) Compute the least square estimated line.

(iii) Compute the correlation coefficient between temperature and the sales of coffee.

(iv) Predict sales of a 90 degree day.

Or

(b) The table below gives the prices of four items – A, B, C and D – sold at a store in 2000

and 2006.

Item Price

2000

$

Price

2006

$

Quantity

2000

Quantity

2006

A 40 10 1,000 800

B 55 25 1,900 5,000

C 95 40 600 3,000

D 250 90 50 200

(i) Using 2000 as the base year, calculate the price relative index for the four items.

(ii) Calculate an unweighted aggregate price index for these items.

(iii) Find the Lasperyres’s weighted aggregate index for these items.

(iv) Find the Paasche index for these items.

(v) Construct a weighted aggregate quantity index using 2000 as the base year price

as the weight.

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